A numerical approach for the stability analysis of open thin-walled beams

2013 ◽  
Vol 48 ◽  
pp. 76-86 ◽  
Author(s):  
Egidio Lofrano ◽  
Achille Paolone ◽  
Giuseppe Ruta
Keyword(s):  
Stability Analysis ◽  
Numerical Approach ◽  
Thin Walled ◽  
The Stability

Analytical and experimental stability analysis of AU4G1 thin-walled tubular workpieces in turning process

2020 ◽  
Vol 234 (6-7) ◽  
pp. 1007-1018 ◽  
Author(s):  
Zied Sahraoui ◽  
Kamel Mehdi ◽  
Moez Ben-Jaber
Keyword(s):  
Stability Analysis ◽  
Feed Rate ◽  
Experimental Studies ◽  
Rake Angle ◽  
Machining Process ◽  
Structural Damping ◽  
Turning Process ◽  
Process Stability ◽  
Thin Walled ◽  
The Stability

The development of the manufacturing-based industries is principally due to the improvement of various machining operations. Experimental studies are important in researches, and their results are also considered useful by the manufacturing industries with their aim to increase quality and productivity. Turning is one of the principal machining processes, and it has been studied since the 20th century in order to prevent machining problems. Chatter or self-excited vibrations represent an important problem and generate the most negative effects on the machined workpiece. To study this cutting process problem, various models were developed to predict stable and unstable cutting conditions. Stability analysis using lobes diagrams became useful to classify stable and unstable conditions. The purpose of this study is to analyze a turning process stability using an analytical model, with three degrees of freedoms, supported and validated with experimental tests results during roughing operations conducted on AU4G1 thin-walled tubular workpieces. The effects of the tubular workpiece thickness, the feed rate and the tool rake angle on the machining process stability will be presented. In addition, the effect of an additional structural damping, mounted inside the tubular workpiece, on the machining process stability will be also studied. It is found that the machining stability process is affected by the tubular workpiece thickness, the feed rate and the tool rake angle. The additional structural damping increases the stability of the machining process and reduces considerably the workpiece vibrations amplitudes. The experimental results highlight that the dynamic behavior of turning process is governed by large radial deformations of the thin-walled workpieces. The influence of this behavior on the stability of the machining process is assumed to be preponderant.

Nonlinear Stability Analysis of Thin-Walled Pier

2013 ◽  
Vol 361-363 ◽  
pp. 1251-1254
Author(s):  
Xiao Mei Dong
Keyword(s):  
Stability Analysis ◽  
Nonlinear Stability ◽  
Shell Element ◽  
Nonlinear Stability Analysis ◽  
Nonlinearity Effect ◽  
Updated Lagrangian Formulation ◽  
Thin Walled ◽  
Displacement Theory ◽  
The Stability ◽  
Updated Lagrangian

Shell element was used to simulate thin-walled piers. Mander constitutive model was adopted for analysis about the material nonlinearity. By finite displacement theory the geometric nonlinearity effect was reckoned in stability analysis based on Updated Lagrangian formulation. Nonlinear stability analysis during different construction stages indicates that the stability of pier in cantilever stage is weakest. Considered the dual non-linearity, the stability coefficient descends distinctly.

Stability Analysis of Rectangular Thin Walled Structure under Nonlinear Distributed Stress

2014 ◽  
Vol 1028 ◽  
pp. 117-121
Author(s):  
De Hui Yu ◽  
Yong Fa Hou ◽  
Jing Sun
Keyword(s):  
Stability Analysis ◽  
Galerkin Method ◽  
Material Properties ◽  
Critical Thickness ◽  
Wall Structure ◽  
Thin Wall ◽  
Nonlinear Stress ◽  
Thin Walled ◽  
The Stability ◽  
Internal Relationship

The stability of rectangular thin wall with 3 simple supported sides and 1 free side, subjected to nonlinear distributed stress, is analyzed. Galerkin method is applied in order to study the internal relationship between the critical thickness and nonlinear stress. Under the same stress circumstance, as the a/b ratio gets larger, the critical thickness for the thin wall structure getting buckled grows too. The influence of different material properties on the critical thickness is also researched. The method proposed in this paper is applicable for more complicated distributed stress and also can provide some reference criterion for design of thin wall structure.

scholarly journals Numerical approach for solving time fractional diffusion equation

2017 ◽  
Vol 7 (3) ◽  
pp. 281-287
Author(s):  
Dilara Altan Koç ◽  
Mustafa Gülsu
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Fractional Diffusion ◽  
Fractional Partial Differential Equations ◽  
Von Neumann ◽  
Liouville Derivative ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Space Method

In this article one of the fractional partial differential equations was solved by finite difference scheme  based on five point and three point central space method with discretization in time. We use between the Caputo and the Riemann-Liouville derivative definition and the Grünwald-Letnikov operator for the fractional calculus. The stability analysis of this scheme is examined by using von-Neumann method. A comparison between exact solutions and numerical solutions is made. Some figures and tables are included.

scholarly journals INVESTIGATION OF THIN-WALLED COLUMN WITH VARIABLE I-SECTION STABILITY USING FINITE ELEMENT METHOD/PLONASIENĖS KINTAMOJO DVITĖJO SKERSPJŪVIO KOLONOS STABILUMO TYRIMAS BAIGTINIŲ ELEMENTŲ METODU

2000 ◽  
Vol 6 (2) ◽  
pp. 69-75
Author(s):  
Michail Samofalov ◽  
Rimantas Kačianauskas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Numerical Experiments ◽  
Relative Length ◽  
Bending Moment ◽  
Relative Height ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
The Stability

Thin-walled structures are widely used in building construction. Stability analysis [1–10] is of major importance to the design of thin-walled structures. This paper deals with the stability analysis of the thin-walled tapered column [11–18]. The aim is to investigate the influence of variation of the web height on the stability of column and combined action of axial force and plane bending moment. Critical state is defined by stability surface obtained by numerical experiments using the finite element method. Mathematical model of the linearised stability problem is presented as algebraic eigenvalue problem (1), where eigenvalues express the critical loading factor (2). Analytical solutions are known for particular cases of separate loading (4), (5). In this paper, the column with variable I-section is presented as assemblage of beam elements with constant section. Thin-walled beam element has 14 degrees of freedom (Fig 1), including linear displacements, rotations and warping displacements. Variation of cross-section of the column (Fig 2) is defined by relative height of web alb, were a and b are the height at the ends of column. Critical state is described by stability surface obtained using numerical experiments. Stability surface presents in the space of relative variation of height a/b, relative length and relative critical force and bending moment . Variation of section influences the critical bending moment only. The influence of finite element number on the with different relative height of web a/b is investigated numerically (Fig 3), and its variation of stability surface is presented in Fig 4. The numerical results show that variation of critical moment to relative web height a/b is linear (Fig 5). The shapes of buckling modes are presented in Fig 6. Variation of stability surface to relative length (6) is presented in Figs 7 and 8 and expressed by the simple expression (6) constructed on the basis of numerical experiments. Finally, the stability model (1) is compared with nonlinear calculations performed using program ANSYS [19] and shell finite elements (Figs 9 and 10).

scholarly journals A framework for linear stability analysis of finite-area vortices

2013 ◽  
Vol 469 (2152) ◽  
pp. 20120709 ◽  
Author(s):  
Alan Elcrat ◽  
Bartosz Protas
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Singular Integrals ◽  
Numerical Approach ◽  
Perturbation Equation ◽  
Constant Vorticity ◽  
Special Cases ◽  
Euler Flows ◽  
The Stability

In this investigation, we revisit the question of linear stability analysis of two-dimensional steady Euler flows characterized by the presence of compact regions with constant vorticity embedded in a potential flow. We give a complete derivation of the linearized perturbation equation which, recognizing that the underlying equilibrium problem is of a free-boundary type, is carried out systematically using methods of shape-differential calculus. Particular attention is given to the proper linearization of contour integrals describing vortex induction. The thus obtained perturbation equation is validated by analytically deducing from it stability analyses of the circular vortex, originally due to Kelvin, and of the elliptic vortex, originally due to Love, as special cases. We also propose and validate a spectrally accurate numerical approach to the solution of the stability problem for vortices of general shape in which all singular integrals are evaluated analytically.

Stability Analysis for the Milling of Thin-Walled Plates

2011 ◽  
Vol 105-107 ◽  
pp. 117-120
Author(s):  
Kai Wu ◽  
Ai Jun Jiang ◽  
Kai Yang
Keyword(s):  
Stability Analysis ◽  
Single Mode ◽  
Critical Element ◽  
Stability Zone ◽  
Main Mode ◽  
Processing Efficiency ◽  
Whole Process ◽  
Stability Lobes ◽  
Thin Walled ◽  
The Stability

In order to restrain the regenerative chatter and improve the processing efficiency of thin-walled parts, stability analysis for the milling of thin-walled parts should be the critical element in the whole process of analysis for thin-walled parts. This paper mainly introduces the stability analysis for the milling of thin-walled plates. The two-dimensional stability lobes of milling of plate plotted, the effect of different modal parameters on the stability of milling of plate is investigated. It is shown that single mode will reduce the range of stability zone of main mode if the stability lobes of single mode are intersectant with that of main mode and the range of stability zone will be larger and the stability lobes will be regular on condition that the mode is symmetrical.

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